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Algorithms 2018, 11(9), 135; https://doi.org/10.3390/a11090135

Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables

Department of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
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Received: 9 August 2018 / Revised: 28 August 2018 / Accepted: 5 September 2018 / Published: 7 September 2018
(This article belongs to the Special Issue Algorithms for Decision Making)
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Abstract

Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches. View Full-Text
Keywords: linguistic cubic hesitant variable; least common multiple number; weighted aggregation operator; linguistic score function; decision making linguistic cubic hesitant variable; least common multiple number; weighted aggregation operator; linguistic score function; decision making
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Ye, J.; Cui, W. Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables. Algorithms 2018, 11, 135.

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